isLattice -- determines if a poset is a lattice

Synopsis

Usage:

i = isLattice P
Inputs:
- P, an instance of the type Poset,
Outputs:
- i, a Boolean value, whether $P$ is a lattice

Description

The poset $P$ is a lattice if every pair of vertices has a unique least upper bound and a unique greatest lower bound, i.e., every pair of vertices has a unique meet and a unique join. Equivalently, the poset $P$ is a lattice if it is both a lower semilattice and an upper semilattice.

Clearly, the $n$ chain and the $n$ booleanLattice are lattices.

i1 : n = 4;

i2 : isLattice chain n

o2 = true

i3 : B = booleanLattice n;

i4 : isLattice B

o4 = true

The middle ranks of the $n$ booleanLattice are not lattices.

i5 : isLattice flagPoset(B, {1,2,3})

o5 = false

Ways to use isLattice :

isLattice(Poset)

For the programmer

The object isLattice is a method function.

isLattice -- determines if a poset is a lattice

Synopsis

Description

See also

Ways to use isLattice :

For the programmer